A computational study of interfacial debonding damage in ®brous composite materials

In this paper the e€ect of ®nite interface strength, and possible debonding, on the macroscopic response of a sample of ®ber-reinforced composite material is computationally investigated via the ®nite element method. The sample consists of several ®bers embedded in a homogeneous matrix, aligned in the longitudinal direction, and randomly distributed in the transverse direction. Plane strain conditions are enforced. Both the matrix and the ®bers are assumed to behave in a linearly elastic manner. The approach is to employ unilateral constraints to model interface strength limits. However, because the debonded surfaces are unknown a priori, and depend on the internal ®elds, the originally linear elastic problem becomes nonlinear, and hence it must be solved in an iterative manner. Accordingly, a nested contact algorithm scheme is developed, based on an active set strategy, to eciently simulate multiple interacting unilateral constraints. The nesting allows the nonlinear problem within a Newton step to be transformed into a sequence of linear sub-problems. Using the algorithm, numerical tests are performed on a widely used Aluminum/Boron ®ber-reinforced composite combination to determine the e€ects of debonding on changes in macroscopic responses as a function of interface strength and loading. It is shown that the amount of debonded surface area correlates perfectly with the loss in the macroscopic sti€ness of the material. This result lends credence to damage evolution laws, for homogenized material models, which employ interface separation surface area as the primary internal damage variable. Ó 1998 Elsevier Science B.V. All rights reserved.